The Potters have taken points from all of their Premier League rivals bar United since they joined the division in 2008.
"I've been desperate for a while to sit down and have a glass of wine with Alex after a game that we've won or drawn to see if he's as happy as he normally is," said Pulis.
"We've taken points off everybody else in the division. The only club we haven't is United. They've beaten us every time we meet. We're all desperate now to put that right."
Stoke are currently in fifth place in the Premier League, while United top the table after their 100% start.